978 Mr A. E. H. Love, On the Motion of a Solid  [Oct. 29, 
Remembering that e, + eg +e, =0, we obtain 
(eC? — a”) (cA® — a”) i (cA® — aw”) (cB’ — a’) 
a 2 
@ 
— 3M’e,= | 
2 2 2 2 
Mee a 
from which ég and e, can be found by cyclical interchanges of the 
letters A, B, C. 
From (138) and (23), we have 
(cA? — a’) (eB? — a") (eC? — a") | WE 0 eu 
Equations (24) and (26) give gv and @’v, so that v is completely 
determined, to a period prés. 
The formule (16), (17), and those which can be derived from 
them by substituting the half-periods wg and w, instead of , give, 
as shown by Halphen, a complete representation of the motion 
when the ellipsoid (2) rolls on one of its tangent planes. He 
further remarks that the discrimination of e,... is made at once by 
observing that these are all real and e,>e,>e,. He shows that 
wu diminished by an odd multiple of the purely imaginary half- 
period @, is real and is determined without ambiguity, and that 
the cosines (A, pM, v)...... as determined by the formule are real 
and less than unity. For this he finds the value of C, in (17) 
to be 
C=C, exp (- ar - ¢) We cidhde. samen (27), 
C, being an arbitrary constant. This is done by using the 
equations 
Mv ea ig 
and N+ p’r —v"g =0 
Hence the orientation of the solid at any time is completely 
determined by the equations (16) and (17), and by those formed 
by substituting therein w, and w, successively for o,. 
10. The translation of the solid is represented by impressing 
upon the system of rolling ellipsoid and plane a velocity whose 
components parallel to the axes of the rotational ellipsoid are 
given by (10), the plane remaining parallel to itself. 
